Yes, but the physical file is on the client, not the server. If I understand correctly, you're programming the server side. You don't care about how the client decides to deal with the PDF once you've sent it. The client probably does write it to a physical file. I don't know, but would hazard a guess that even the plug-in does that.
Even more, as a server-side writer, you probably don't actually tell the client machine specifically to use Adobe Reader (plugin or otherwise) to view the PDF. The client machine decides for itself. The client machine might be using one of the very fine products of Global Graphics, for instance
this one. Sorry, blatant advertising.
[ April 18, 2007: Message edited by: Peter Chase ]